A two-stroke engine of the above kind is disclosed in U.S. Pat. No. 6,216,650. The bypass channel, which supplies clean air, opens via a membrane valve into the transfer channel which is configured as a radially open channel. The radial opening of the transfer channel is closed by a valve housing which carries the membrane valve and which is to be mounted on the cylinder. This requires a significant manufacturing and assembly effort because the valve plate is to be mounted close to the transfer channel.